Implication details
Claim: A category is accessible and is complete if and only if it is locally presentable.
Proof: This follows from one of the equivalent formulations of locally presentable categories.
This implication has a dual.
Show 50 categories using this implication
- trivial category
- category of abelian groups
- category of finitely generated abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- simplex category
- category of fields
- category of countable groups
- category of finitely generated groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of extended metric spaces
- category of monoids
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets
- category of preordered sets
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers
- category of quivers with finite components
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of rings
- category of rngs
- category of semigroups
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- category of large families of sets which are mostly empty
- category of sets with finite-to-one maps
- indiscrete category of sets
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of large vector spaces over a large field with a small basis
- category of Z-sets
- preordered set of integers w.r.t. divisibility
- forked commutative square
- real interval [0,1]
- category of simplicial sets
- walking coreflexive pair
- walking isomorphism